Bergman-Hartogs域上的Roper-Suffridge延拓算子  

The Generalized Roper-Suffridge Operators on Bergman-Hartogs Domains

作　　者：崔艳艳 王朝君 刘浩[2] Yan Yan CUI;Chao Jun WANG;Hao LIU(College of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466001,P.R.China;Institute of Contemporary Mathematics,Henan University,Kaifeng 475001,P.R.China)

机构地区：[1]周口师范学院数学与统计学院,周口466001 [2]河南大学现代数学研究所,开封475001

出　　处：《数学学报（中文版）》2021年第5期787-800,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11271359,11471098);河南省教育厅科学技术研究重点项目(17A110041,19B110016);周口师范学院科研创新基金项目(ZKNUA201805)。

摘　　要：本文给出多复变数空间中构造具有特殊几何性质的双全纯映照的新方法,讨论了Bergman-Hartogs域上推广的Roper-Suffridge算子的性质,并利用Bergman-Hartogs域的特征及双全纯映照子族的几何性质,证明推广的Roper-Suffridge算子在Bergman-Hartogs域上及在不同的条件下保持强α次殆β型螺形映照、复数入阶殆星形映照及S_(Ω)~*(β,A,B)的几何性质.由此得到简化后的算子具有同样的性质.New approaches to construct biholomorphic mappings which have special geometric properties in several complex variables are obtained in this paper.The properties of the generalized Roper-Suffridge operators on Bergman-Hartogs domains are mainly discussed.With the characteristics of Bergman-Hartogs domains and the geometric properties of subclasses of biholomorphic mappings,the generalized RoperSuffridge operators are proved to preserve the properties of strong and almost spirallike mappings of typeβand orderα,almost starlike mapping of complex orderλ,SΩ*(β,A,B)on Bergman-Hartogs domains under different conditions.Sequentially,the same conclusions are obtained for the reduced Roper-Suffridge extension operators.

关 键 词：ROPER-SUFFRIDGE算子 螺形映照 Bergman-Hartogs域 

分 类 号：O174.56[理学—数学]